This is a summary of the primary figures and tests I have completed for Chapter 2 as of my oral exams (April 2018), as well as accompanying notes and questions.

1 Correlations among predictor variables

1.1 Benthic variables

1.2 Selected fish and benthic variables

2 PCAs

2.1 All predictors

predictors <- site.sum %>% select(cover_LC,cover_TA,canopy_MA,canopy_TA,rugosity) # should it matter if I use site level summary data vs. full follow dataset (where site-level data has been joined?)
pca <- prcomp(na.omit(predictors),center = TRUE,scale. = TRUE) 
summary(pca)
## Importance of components:
##                           PC1    PC2     PC3     PC4     PC5
## Standard deviation     1.7912 1.1130 0.60454 0.33002 0.27993
## Proportion of Variance 0.6417 0.2478 0.07309 0.02178 0.01567
## Cumulative Proportion  0.6417 0.8894 0.96255 0.98433 1.00000
plot(pca,type="l")

ggbiplot(pca, obs.scale = 1, var.scale = 1, groups=site.sum$Island, ellipse = TRUE, circle = TRUE, varname.size = 2) + scale_color_manual(name="Island", values=c("navy", "darkseagreen", "slategray2")) + theme(legend.direction = 'horizontal', legend.position = 'top') + theme_minimal()

ggsave("pca_benth.png")
## Saving 7 x 5 in image

2.2 Benthic predictors

3 Grazing differences among islands

3.1 Feeding rates

##             Df   Sum Sq Mean Sq F value   Pr(>F)    
## Island       2 18202819 9101410   22.33 1.38e-08 ***
## Residuals   89 36271681  407547                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = FR ~ Island, data = vet20init)
## 
## $Island
##                      diff       lwr       upr     p adj
## Barbuda-Antigua -80.69712 -618.6796  457.2854 0.9320204
## Bonaire-Antigua 892.24038  464.1018 1320.3789 0.0000097
## Bonaire-Barbuda 972.93750  544.7990 1401.0760 0.0000015

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2  0.0535 0.9479
##       89
##              Df  Sum Sq Mean Sq F value   Pr(>F)    
## Island        2 3765399 1882699   25.35 5.73e-10 ***
## Residuals   125 9283349   74267                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = FR ~ Island, data = vir20init, white.adjust = TRUE)
## 
## $Island
##                      diff       lwr      upr     p adj
## Barbuda-Antigua 315.65455  164.6361 466.6730 0.0000068
## Bonaire-Antigua 364.50714  234.9929 494.0214 0.0000000
## Bonaire-Barbuda  48.85258 -105.4620 203.1672 0.7336418

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value Pr(>F)
## group   2  2.2444 0.1102
##       125

3.2 Bite rates

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Island       2  0.631  0.3155   3.149 0.0477 *
## Residuals   89  8.917  0.1002                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = BR ~ Island, data = vet20init, white.adjust = TRUE)
## 
## $Island
##                       diff         lwr       upr     p adj
## Barbuda-Antigua 0.05995462 -0.20679424 0.3267035 0.8539726
## Bonaire-Antigua 0.19986289 -0.01242184 0.4121476 0.0693799
## Bonaire-Barbuda 0.13990827 -0.07237646 0.3521930 0.2635451

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value   Pr(>F)    
## group  2  10.329 9.25e-05 ***
##       89                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##              Df Sum Sq Mean Sq F value Pr(>F)
## Island        2  0.018 0.00881   0.176  0.839
## Residuals   125  6.248 0.04998
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = BR ~ Island, data = vet20init, white.adjust = TRUE)
## 
## $Island
##                       diff         lwr       upr     p adj
## Barbuda-Antigua 0.05995462 -0.20679424 0.3267035 0.8539726
## Bonaire-Antigua 0.19986289 -0.01242184 0.4121476 0.0693799
## Bonaire-Barbuda 0.13990827 -0.07237646 0.3521930 0.2635451

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value   Pr(>F)    
## group   2  10.278 7.37e-05 ***
##       125                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

3.3 Fraction of time spent grazing

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Island       2  0.631  0.3155   3.149 0.0477 *
## Residuals   89  8.917  0.1002                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value   Pr(>F)    
## group  2  10.329 9.25e-05 ***
##       89                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##              Df Sum Sq Mean Sq F value Pr(>F)
## Island        2  0.018 0.00881   0.176  0.839
## Residuals   125  6.248 0.04998

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value   Pr(>F)    
## group   2  10.278 7.37e-05 ***
##       125                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

3.4 Grazing intensity

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## Island       2   1290   645.1   6.947 0.00161 **
## Residuals   84   7801    92.9                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 5 observations deleted due to missingness
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = for.bites ~ Island, data = vet20init, white.adjust = TRUE)
## 
## $Island
##                      diff       lwr       upr     p adj
## Barbuda-Antigua 0.4163004 -8.439851  9.272452 0.9930895
## Bonaire-Antigua 8.5208532  1.696287 15.345420 0.0104552
## Bonaire-Barbuda 8.1045528  1.070381 15.138725 0.0198160

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2  1.4821  0.233
##       84
##              Df Sum Sq Mean Sq F value   Pr(>F)    
## Island        2    813   406.7   12.46 1.26e-05 ***
## Residuals   115   3753    32.6                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 10 observations deleted due to missingness
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = for.bites ~ Island, data = vir20init, white.adjust = TRUE)
## 
## $Island
##                     diff        lwr      upr     p adj
## Barbuda-Antigua 3.431446  0.1293407 6.733552 0.0397136
## Bonaire-Antigua 5.966846  3.1227232 8.810969 0.0000067
## Bonaire-Barbuda 2.535400 -0.7532184 5.824018 0.1642219

## Levene's Test for Homogeneity of Variance (center = median)
##        Df F value   Pr(>F)   
## group   2  5.3717 0.005885 **
##       115                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4 Bivariate plots

4.1 Grazing as a function of fish size

Due to the lack of larger fish in Barbuda, these length-based relationships focus on comparisons between Antigua and Bonaire

vetAB <- vetvirAB %>% filter(Species.Code=="qup")
vet_fr <- lm(FR~Length.cm+Island,data=vetAB)
anova(vet_fr)
## Analysis of Variance Table
## 
## Response: FR
##            Df   Sum Sq  Mean Sq F value    Pr(>F)    
## Length.cm   1  4967075  4967075  15.165 0.0001263 ***
## Island      1 27363708 27363708  83.545 < 2.2e-16 ***
## Residuals 251 82210785   327533                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
virAB <- vetvirAB %>% filter(Species.Code=="stop")
vir_fr <- lm(FR~Length.cm+Island,data=virAB)
anova(vir_fr)
## Analysis of Variance Table
## 
## Response: FR
##            Df   Sum Sq Mean Sq F value Pr(>F)    
## Length.cm   1    18101   18101  0.2649 0.6072    
## Island      1  5899425 5899425 86.3223 <2e-16 ***
## Residuals 280 19135708   68342                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

4.2 Grazing impact as a function of scarid biomass

# Comparisons with published data

# calculate predicted feeding rates from Bruggemann/Bozec for boxplot reference lines:
FR.vet20=3329-33*20
FR.vir20=1089-17*20-56
# Observed Antigua feeding rate equation:
ANUinit.vir <- data %>% filter(Island=="Antigua"&Phase=="i"&Species.Code=="stop")
ANUinit.vet <- data %>% filter(Island=="Antigua"&Phase=="i"&Species.Code=="qup")
FR.anu.vir <- lm(FR~Length.cm, data=ANUinit.vir)
FR.anu.vet <- lm(FR~Length.cm, data=ANUinit.vet)
summary(FR.anu.vet)
## 
## Call:
## lm(formula = FR ~ Length.cm, data = ANUinit.vet)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -833.8 -513.2 -102.2  436.9 1391.3 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  1047.76     460.25   2.277   0.0282 *
## Length.cm     -11.89      17.66  -0.673   0.5047  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 617.4 on 40 degrees of freedom
## Multiple R-squared:  0.0112, Adjusted R-squared:  -0.01352 
## F-statistic: 0.4531 on 1 and 40 DF,  p-value: 0.5047
#FR.anu.vet = 1047-12*L
summary(FR.anu.vir)
## 
## Call:
## lm(formula = FR ~ Length.cm, data = ANUinit.vir)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -315.25 -173.55  -63.47  138.46  589.65 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  445.037    108.268   4.111 9.31e-05 ***
## Length.cm     -8.112      4.472  -1.814   0.0733 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 211.3 on 82 degrees of freedom
## Multiple R-squared:  0.03858,    Adjusted R-squared:  0.02685 
## F-statistic:  3.29 on 1 and 82 DF,  p-value: 0.07335
#FR.anu.vir = 445-8*L
# Observed Bonaire feeding rate equation:
BONinit.vir <- data %>% filter(Island=="Bonaire"&Phase=="i"&Species.Code=="stop")
BONinit.vet <- data %>% filter(Island=="Bonaire"&Phase=="i"&Species.Code=="qup")
FR.bon.vir <- lm(FR~Length.cm, data=BONinit.vir)
FR.bon.vet <- lm(FR~Length.cm, data=BONinit.vet)

summary(FR.bon.vet)
## 
## Call:
## lm(formula = FR ~ Length.cm, data = BONinit.vet)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1601.66  -332.61   -12.37   397.51  2137.87 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1347.802    378.678   3.559 0.000552 ***
## Length.cm      9.764     15.193   0.643 0.521792    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 601.9 on 109 degrees of freedom
## Multiple R-squared:  0.003775,   Adjusted R-squared:  -0.005365 
## F-statistic: 0.413 on 1 and 109 DF,  p-value: 0.5218
#FR.bon.vet = 1347+10*L
summary(FR.bon.vir)
## 
## Call:
## lm(formula = FR ~ Length.cm, data = BONinit.vir)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -655.76 -153.40    9.15  199.52  696.42 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1057.197    159.987   6.608 2.25e-09 ***
## Length.cm    -17.454      6.153  -2.837  0.00557 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 290.3 on 95 degrees of freedom
## Multiple R-squared:  0.07809,    Adjusted R-squared:  0.06838 
## F-statistic: 8.047 on 1 and 95 DF,  p-value: 0.005572
#FR.bon.vir = 1057-15*L

4.3 adding predicted feeding rates and bite sizes from standard equations

Bite sizes as predicted by Bruggemann/Bozec: S. vetula: BS.vet=4.01310^-4L^2 S. viride: BS.vir=5.25710^-4L^2

Feeding rates as predicted by Bruggemann/Bozec S. vetula: FR.vet=3329-33L S. viride: FR.vir=1089-17L-56 (extra term because phase modifier is not used here (i=1))

Feeding rates as predicted by observed Bonaire data: S. vetula: FR.bon.vet = 1347+10L S. viride: FR.bon.vir = 1057-15L

Feeding rates as predicted by observed Antigua data: S. vetula: FR.anu.vet = 1047-12L S. viride: FR.anu.vir = 445-8L

4.4 adding predicted feeding rates from observed relationships

# Antigua
feedingrates.vet.ANU <- data %>% filter(Species.Code=="qup"&Phase=="i"&Island=="Antigua") %>% mutate(FR.personal=1047-12*Length.cm) %>% mutate(FR.standard=3329-33*Length.cm) %>% mutate(BS=4.013*10^-4*Length.cm^2)
feedingrates.vir.ANU <- data %>% filter(Species.Code=="stop"&Phase=="i"&Island=="Antigua") %>% mutate(FR.personal = 445-8*Length.cm) %>% mutate(FR.standard=1089-17*Length.cm-56) %>% mutate(BS=5.257*10^-4*Length.cm^2)

# Bonaire
feedingrates.vet.BON <- data %>% filter(Species.Code=="qup"&Phase=="i"&Island=="Bonaire") %>% mutate(FR.personal=1047-12*Length.cm) %>% mutate(FR.standard=1347+10*Length.cm) %>% mutate(BS=4.013*10^-4*Length.cm^2)
feedingrates.vir.BON <- data %>% filter(Species.Code=="stop"&Phase=="i"&Island=="Bonaire") %>% mutate(FR.personal = 1057-15*Length.cm) %>% mutate(FR.standard=1089-17*Length.cm-56) %>% mutate(BS=5.257*10^-4*Length.cm^2)

feedingrates <- bind_rows(feedingrates.vir.ANU,feedingrates.vet.ANU,feedingrates.vir.BON,feedingrates.vet.BON) %>% mutate(AG.personal=FR.personal*BS) %>% mutate(AG.standard=FR.standard*BS)

areagrazed.site <- feedingrates %>% group_by(Site,Island) %>% dplyr::summarize(personal=sum(AG.personal)/1000,standard=sum(AG.standard)/1000)

areagrazed.site <- as.data.frame(areagrazed.site)
AG <- melt(areagrazed.site, id=c("Site","Island")) %>% dplyr::rename("data.source"=variable, "area.grazed"=value)
AG.ANU <- AG %>% filter(Island=="Antigua")
ggplot(data=AG.ANU, aes(x=Site, y=area.grazed, fill=data.source)) +
    geom_bar(stat="identity", position=position_dodge()) + theme_bw() + scale_fill_manual(values=c("black","lightslategrey"),name=expression(paste("Feeding rates \n obtained from:")),breaks=c("personal", "standard"), labels=c("fished data", "unfished data")) + labs(y=expression(Area~Grazed~(m^2/hr)), title=("Predicted site-level grazing impact of Antiguan scarids")) + theme(plot.title = element_text(hjust = 0.5)) + theme(axis.text.x = element_text(angle = 45, hjust = 1))

ggsave("areagrazed.png")
## Saving 7 x 5 in image

5 Competition

## Saving 7 x 5 in image

## Saving 7 x 5 in image

6 GAMMs

6.1 Scarus vetula

6.1.1 Feeding rates

vetinit <- data2 %>% filter(Species.Code=="qup" & Phase=="i")
vetinit <- vetinit %>% dplyr::rename(PC1='PC1.x',PC2='PC2.x')
gamm<-gamm(FR~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=vetinit, random=list(Island=~1),method="REML")
summary(gamm$gam) # only PC1 and PC2 are significant, length slightly, scar.BM is not
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## FR ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   1274.6       42.4   30.06   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df      F  p-value    
## s(Length.cm) 4.452  4.452  3.260   0.0269 *  
## s(scar.BM)   1.000  1.000  2.993   0.0855 .  
## s(PC1)       1.492  1.492 18.228 1.64e-06 ***
## s(PC2)       2.833  2.833  9.709 1.11e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.431   
##   Scale est. = 3.0742e+05  n = 171
AIC(gamm$lme)
## [1] 2628.616
plot(gamm$gam,pages=1)

6.1.2 Fraction of time spent grazing

gamm<-gamm(g.frac~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=vetinit, random=list(Island=~1),method="REML")
summary(gamm$gam) # PC1 and PC2 are most significant, length is significant, scar.BM is almost significant
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## g.frac ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.41632    0.01252   33.26   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df      F  p-value    
## s(Length.cm) 5.370  5.370  5.419 7.27e-05 ***
## s(scar.BM)   1.000  1.000  7.071  0.00862 ** 
## s(PC1)       1.000  1.000 40.097 1.95e-09 ***
## s(PC2)       3.535  3.535 12.264 3.60e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.484   
##   Scale est. = 0.026789  n = 171
AIC(gamm$lme)
## [1] -64.97683
plot(gamm$gam,pages=1)

6.1.3 Grazing intensity

gamm<-gamm(for.bites~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=vetinit, random=list(Island=~1),method="REML")
summary(gamm$gam) # very low R2, only PC1 and scar.BM significant
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## for.bites ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  12.4857     0.6427   19.43   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df     F p-value  
## s(Length.cm) 1.000  1.000 0.195  0.6592  
## s(scar.BM)   1.000  1.000 2.093  0.1500  
## s(PC1)       1.000  1.000 5.748  0.0177 *
## s(PC2)       1.543  1.543 0.694  0.3418  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =   0.17   
##   Scale est. = 66.495    n = 161
AIC(gamm$lme)
## [1] 1144.704
plot(gamm$gam,pages=1)

6.2 Sparisoma viride

6.2.1 Feeding rates

virinit <- data2 %>% filter(Species.Code=="stop" & Phase=="i")
virinit <- virinit %>% dplyr::rename(PC1='PC1.x',PC2='PC2.x')
gamm<-gamm(FR~s(Length.cm)+s(scar.BM)+s(PC1)+s(PC2), family=gaussian(link=identity),data=virinit, random=list(Island=~1),method="REML")
summary(gamm$gam) #PC1, length, and scar.BM are significant predictors
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## FR ~ s(Length.cm) + s(scar.BM) + s(PC1) + s(PC2)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   466.37      17.92   26.03   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##               edf Ref.df      F  p-value    
## s(Length.cm) 1.00   1.00 15.856 9.35e-05 ***
## s(scar.BM)   1.00   1.00  4.696   0.0313 *  
## s(PC1)       3.12   3.12 17.807 1.22e-10 ***
## s(PC2)       1.00   1.00  1.796   0.1816    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.332   
##   Scale est. = 69343     n = 216
AIC(gamm$lme)
## [1] 3002.844
plot(gamm$gam,pages=1)

6.2.2 Fraction of time spent grazing

gamm<-gamm(g.frac~s(Length.cm)+s(scar.BM)+s(PC1), family=gaussian(link=identity),data=virinit, random=list(Island=~1),method="REML")
summary(gamm$gam) #PC1, length, and scar.BM are significant predictors
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## g.frac ~ s(Length.cm) + s(scar.BM) + s(PC1)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.38137    0.01609    23.7   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df      F  p-value    
## s(Length.cm) 1.000  1.000  9.411  0.00243 ** 
## s(scar.BM)   1.328  1.328  4.457  0.09082 .  
## s(PC1)       3.131  3.131 17.261 2.56e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.318   
##   Scale est. = 0.055926  n = 216
AIC(gamm$lme)
## [1] 33.45903
plot(gamm$gam,pages=1)

6.2.3 Grazing intensity

gamm<-gamm(for.bites~s(Length.cm)+s(scar.BM)+s(PC1), family=gaussian(link=identity),data=virinit, random=list(Island=~1),method="REML")
summary(gamm$gam) # no significant predictors (scar.BM almost), low r2
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## for.bites ~ s(Length.cm) + s(scar.BM) + s(PC1)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   6.7838     0.4073   16.66   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                edf Ref.df     F  p-value    
## s(Length.cm) 1.000  1.000 2.690 0.102643    
## s(scar.BM)   1.000  1.000 0.021 0.885774    
## s(PC1)       3.034  3.034 6.959 0.000168 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.175   
##   Scale est. = 32.178    n = 194
AIC(gamm$lme)
## [1] 1240.743
plot(gamm$gam,pages=1)